Gabriel Ng

Large fields are an important class of fields in algebraic geometry and Galois theory, and are an active topic of study in their own right in model theory. Differentially large fields were introduced by León Sánchez and Tressl as an analogue for large fields in differential algebra. This project will develop understanding of the model-theoretic and algebraic properties of differentially large fields in full generality. We will apply new tools developed in the study of abstract Taylor morphisms to generalise results from characteristic 0 to positive characteristic. We also aim to apply tools from the study of differentially henselian fields in order to study the model-theoretic properties of differentially large fields, in particular to characterise the model-theoretic properties of a differentially large field. We will study the algebraic properties of certain classes of differentially large fields, and build connections to differential algebraic geometry and Galois theory.